Self Studies

Set Theory Test...

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  • Question 1
    1 / -0

    If two sets AA and BB are having 9999 elements in common, then the number of ordered pairs common to each of the sets AxBAxB and BxABxA are

  • Question 2
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    If X={1,2,3,4,5,6,7,8,9,10}X =\{1,2,3,4,5,6,7,8,9, 10\} is the universal set andA={1,2,3,4},B={2,4,6,8},C={3,4,5,6} A= \{1, 2, 3,4\}, B= \{2,4,6,8\}, C= \{3,4,5,6\}  verify the following.
    (a) A(BC)=(AB)CA \cup (B\cup C) = (A \cup B) \cup C
    (b)A(BC)=(AB)(AC)A \cap (B\cup C) = (A \cap B) \cup (A \cap C)
    (c) (A)=A(A')' =A

  • Question 3
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    S1:(pq)V(qp)S_1:(p\Rightarrow q) V ( q \Rightarrow p ) is a tautology.
    S2:((pq)V(qp))S_2: ((p\Rightarrow q) V ( q \Rightarrow p)) is a fallacy

  • Question 4
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    IfA={(x,y)x2+y24}andIf\,A = \left\{ {\left( {x,y} \right)\,\left| {{x^2} + {y^2} \le \left. 4 \right\}\,and} \right.} \right.
    B={(x,y)(x3)2+y24}andtheB = \left\{ {\left( {x,y} \right)\,\left| {{{(x - 3)}^2} + {y^2}} \right. \le \left. 4 \right\}} \right.\,and\,the
    pointP(a,12)belongstothesetBApo{\mathop{\rm int}} \,P\left( {a,\frac{1}{2}} \right)\,belongs\,to\,the\,set\,B - A then the set of possible real values of aa is

  • Question 5
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    In a selection process, a hundred candidate participate in Group Discussion sessions (GD) and Personal Interview (PI). The possibilities of a candidate's good performance in GD and in PI are independent of each other. It was found that 2020 candidates were good in GD and 3030 were good in PI. The number of candidates good in both GD and PI is expected to be about:

  • Question 6
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    If ABA \subset B, then

  • Question 7
    1 / -0

    The set of all xx for which 1+logx<x1 + \log x < x is

  • Question 8
    1 / -0

    s={xN:2+log2x+1 >1log1/24x2}s = \{ x \in N:2 + {\log _2}\sqrt {x + 1}  > 1 - {\log _{1/2}}\sqrt {4 - {x^2}} \} , then

  • Question 9
    1 / -0

    If α,ξ,η\alpha,\xi,\eta are non-empty sets then:

  • Question 10
    1 / -0

    For any two sets A and B, A' - B' is equal to

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